I think, A, you should not ask the grandparents to chip in.
B, I don't think you should invite the cousins if their mother is not included. I get that you feel bad that they may not get to go due to Casey's finances, but I think it's awkward to invite your neighbors, their mother, their kids, and Casey's kids, but not Casey. Also, I would want to share in my kids' first WDW experience, and having someone take them because they can afford it and I can't would make me feel awful. Please don't interpret that as that I think you are bad for thinking about it, because it's a wonderful and generous offer.
C, I think if you offer airfare and accomodations, and possibly theme park tickets, but asked everyone to pay for their meal plans, that might allow you to invite everyone? And since you'd be using the WDW vacation club points and airfare miles, it might make it seem less like charity for Casey (that may or may not even be an issue, but I know a lot of people would be too proud to accept something like that).
I hope things work out, it sounds like a lot of fun!